%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN143-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:20 AM UTC 2025
% Result : Unsatisfiable 0.77s 0.94s
% Output : Proof 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 134
% Syntax : Number of formulae : 428 ( 329 unt; 0 typ; 0 def)
% Number of atoms : 565 ( 545 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 167 ( 49 ~; 45 |; 0 &)
% ( 73 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 6 con; 0-4 aty)
% Number of variables : 517 ( 473 !; 0 ?; 517 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(m5_type,type,
m5: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(m4_type,type,
m4: ( $i * $i ) > $i ).
tff(e_type,type,
e: $i ).
tff(s4_type,type,
s4: $i > $i ).
tff(l1_type,type,
l1: ( $i * $i ) > $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(p3_type,type,
p3: ( $i * $i * $i ) > $i ).
tff(q0_type,type,
q0: ( $i * $i ) > $i ).
tff(k2_type,type,
k2: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $i ).
tff(r0_type,type,
r0: $i > $i ).
tff(l2_type,type,
l2: ( $i * $i ) > $i ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(p0_type,type,
p0: ( $i * $i ) > $i ).
tff(s1_type,type,
s1: $i > $i ).
tff(s3_type,type,
s3: ( $i * $i ) > $i ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $i ).
tff(l0_type,type,
l0: $i > $i ).
tff(s2_type,type,
s2: $i > $i ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $i ).
tff(s0_type,type,
s0: $i > $i ).
tff(k0_type,type,
k0: $i > $i ).
tff(1,plain,
^ [B: $i] :
refl(( ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true )
<=> ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i] : ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true )
<=> ! [B: $i] : ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i] : ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true )
<=> ! [B: $i] : ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i] : ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_305) ).
tff(5,plain,
! [B: $i] : ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i] : ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i] : ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i] : ( ifeq(s4(B),true,ifeq(m4(e,e),true,m5(B,B),true),true) = true )
| ( ifeq(s4(d),true,ifeq(m4(e,e),true,m5(d,d),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(s4(d),true,ifeq(m4(e,e),true,m5(d,d),true),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,s4(d),true) = s4(d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(true,true,s4(d),true) = s4(d),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,l1(d,d),true) = l1(d,d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
ifeq(true,true,l1(d,d),true) = l1(d,d),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
( ( n0(c,d) = true )
<=> ( n0(c,d) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
n0(c,d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
tff(23,plain,
n0(c,d) = true,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
true = n0(c,d),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
ifeq(true,true,l1(d,d),true) = ifeq(n0(c,d),true,l1(d,d),true),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
ifeq(n0(c,d),true,l1(d,d),true) = ifeq(true,true,l1(d,d),true),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
^ [H: $i,G: $i] :
refl(( ( ifeq(n0(H,G),true,l1(G,G),true) = true )
<=> ( ifeq(n0(H,G),true,l1(G,G),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true )
<=> ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true )
<=> ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_002) ).
tff(31,plain,
! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true )
| ( ifeq(n0(c,d),true,l1(d,d),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
ifeq(n0(c,d),true,l1(d,d),true) = true,
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
true = ifeq(n0(c,d),true,l1(d,d),true),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
true = l1(d,d),
inference(transitivity,[status(thm)],[36,26,20]) ).
tff(38,plain,
ifeq(true,true,s4(d),true) = ifeq(l1(d,d),true,s4(d),true),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
ifeq(l1(d,d),true,s4(d),true) = ifeq(true,true,s4(d),true),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
s4(d) = ifeq(true,true,s4(d),true),
inference(symmetry,[status(thm)],[18]) ).
tff(41,plain,
s4(d) = ifeq(l1(d,d),true,s4(d),true),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p3(d,d,d),true) = p3(d,d,d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
ifeq(true,true,p3(d,d,d),true) = p3(d,d,d),
inference(unit_resolution,[status(thm)],[42,16]) ).
tff(44,plain,
( ( q0(e,d) = true )
<=> ( q0(e,d) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
q0(e,d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(46,plain,
q0(e,d) = true,
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
true = q0(e,d),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
ifeq(true,true,p3(d,d,d),true) = ifeq(q0(e,d),true,p3(d,d,d),true),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
ifeq(q0(e,d),true,p3(d,d,d),true) = ifeq(true,true,p3(d,d,d),true),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(q0(e,d),true,p3(d,d,d),true),true) = ifeq(q0(e,d),true,p3(d,d,d),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
ifeq(true,true,ifeq(q0(e,d),true,p3(d,d,d),true),true) = ifeq(q0(e,d),true,p3(d,d,d),true),
inference(unit_resolution,[status(thm)],[50,16]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,k2(b,b),true) = k2(b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
ifeq(true,true,k2(b,b),true) = k2(b,b),
inference(unit_resolution,[status(thm)],[52,16]) ).
tff(54,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,q1(b,b,b),true) = q1(b,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
ifeq(true,true,q1(b,b,b),true) = q1(b,b,b),
inference(unit_resolution,[status(thm)],[54,16]) ).
tff(56,plain,
( ( r0(b) = true )
<=> ( r0(b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
r0(b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
tff(58,plain,
r0(b) = true,
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
true = r0(b),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
ifeq(true,true,q1(b,b,b),true) = ifeq(r0(b),true,q1(b,b,b),true),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
ifeq(r0(b),true,q1(b,b,b),true) = ifeq(true,true,q1(b,b,b),true),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ( ifeq(r0(b),true,q1(b,b,b),true) = true )
<=> ( ifeq(r0(b),true,q1(b,b,b),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
ifeq(r0(b),true,q1(b,b,b),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_120) ).
tff(64,plain,
ifeq(r0(b),true,q1(b,b,b),true) = true,
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
true = ifeq(r0(b),true,q1(b,b,b),true),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
true = q1(b,b,b),
inference(transitivity,[status(thm)],[65,61,55]) ).
tff(67,plain,
ifeq(true,true,k2(b,b),true) = ifeq(q1(b,b,b),true,k2(b,b),true),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
ifeq(q1(b,b,b),true,k2(b,b),true) = ifeq(true,true,k2(b,b),true),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
^ [A: $i,J: $i] :
refl(( ( ifeq(q1(A,J,J),true,k2(J,J),true) = true )
<=> ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true )
<=> ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true )
<=> ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_129) ).
tff(73,plain,
! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ~ ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true )
| ( ifeq(q1(b,b,b),true,k2(b,b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
ifeq(q1(b,b,b),true,k2(b,b),true) = true,
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
true = ifeq(q1(b,b,b),true,k2(b,b),true),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
true = k2(b,b),
inference(transitivity,[status(thm)],[78,68,53]) ).
tff(80,plain,
ifeq(true,true,ifeq(q0(e,d),true,p3(d,d,d),true),true) = ifeq(k2(b,b),true,ifeq(q0(e,d),true,p3(d,d,d),true),true),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
ifeq(k2(b,b),true,ifeq(q0(e,d),true,p3(d,d,d),true),true) = ifeq(true,true,ifeq(q0(e,d),true,p3(d,d,d),true),true),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
^ [I: $i,J: $i,H: $i] :
refl(( ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true )
<=> ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true )
<=> ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true )
<=> ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_252) ).
tff(86,plain,
! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ~ ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true )
| ( ifeq(k2(b,b),true,ifeq(q0(e,d),true,p3(d,d,d),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
ifeq(k2(b,b),true,ifeq(q0(e,d),true,p3(d,d,d),true),true) = true,
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
true = ifeq(k2(b,b),true,ifeq(q0(e,d),true,p3(d,d,d),true),true),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
l1(d,d) = ifeq(true,true,l1(d,d),true),
inference(symmetry,[status(thm)],[20]) ).
tff(93,plain,
l1(d,d) = p3(d,d,d),
inference(transitivity,[status(thm)],[92,25,35,91,81,51,49,43]) ).
tff(94,plain,
ifeq(l1(d,d),true,s4(d),true) = ifeq(p3(d,d,d),true,ifeq(l1(d,d),true,s4(d),true),true),
inference(monotonicity,[status(thm)],[93,41]) ).
tff(95,plain,
ifeq(p3(d,d,d),true,ifeq(l1(d,d),true,s4(d),true),true) = ifeq(l1(d,d),true,s4(d),true),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true )
<=> ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_299) ).
tff(100,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true )
| ( ifeq(p3(d,d,d),true,ifeq(l1(d,d),true,s4(d),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
ifeq(p3(d,d,d),true,ifeq(l1(d,d),true,s4(d),true),true) = true,
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
true = ifeq(p3(d,d,d),true,ifeq(l1(d,d),true,s4(d),true),true),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
true = s4(d),
inference(transitivity,[status(thm)],[105,95,39,18]) ).
tff(107,plain,
ifeq(true,true,ifeq(m4(e,e),true,m5(d,d),true),true) = ifeq(s4(d),true,ifeq(m4(e,e),true,m5(d,d),true),true),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(m4(e,e),true,m5(d,d),true),true) = ifeq(m4(e,e),true,m5(d,d),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
ifeq(true,true,ifeq(m4(e,e),true,m5(d,d),true),true) = ifeq(m4(e,e),true,m5(d,d),true),
inference(unit_resolution,[status(thm)],[108,16]) ).
tff(110,plain,
ifeq(m4(e,e),true,m5(d,d),true) = ifeq(true,true,ifeq(m4(e,e),true,m5(d,d),true),true),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,m4(e,e),true) = m4(e,e) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
ifeq(true,true,m4(e,e),true) = m4(e,e),
inference(unit_resolution,[status(thm)],[111,16]) ).
tff(113,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,l2(e,e),true) = l2(e,e) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
ifeq(true,true,l2(e,e),true) = l2(e,e),
inference(unit_resolution,[status(thm)],[113,16]) ).
tff(115,plain,
( ( m0(a,e,e) = true )
<=> ( m0(a,e,e) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
m0(a,e,e) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
tff(117,plain,
m0(a,e,e) = true,
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
true = m0(a,e,e),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
ifeq(true,true,l2(e,e),true) = ifeq(m0(a,e,e),true,l2(e,e),true),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
ifeq(m0(a,e,e),true,l2(e,e),true) = ifeq(true,true,l2(e,e),true),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
l2(e,e) = ifeq(true,true,l2(e,e),true),
inference(symmetry,[status(thm)],[114]) ).
tff(122,plain,
l2(e,e) = ifeq(m0(a,e,e),true,l2(e,e),true),
inference(transitivity,[status(thm)],[121,119]) ).
tff(123,plain,
^ [X: $i] :
refl(( ( p0(b,X) = true )
<=> ( p0(b,X) = true ) )),
inference(bind,[status(th)],[]) ).
tff(124,plain,
( ! [X: $i] : ( p0(b,X) = true )
<=> ! [X: $i] : ( p0(b,X) = true ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
( ! [X: $i] : ( p0(b,X) = true )
<=> ! [X: $i] : ( p0(b,X) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,axiom,
! [X: $i] : ( p0(b,X) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
tff(127,plain,
! [X: $i] : ( p0(b,X) = true ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [X: $i] : ( p0(b,X) = true ),
inference(skolemize,[status(sab)],[127]) ).
tff(129,plain,
! [X: $i] : ( p0(b,X) = true ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
( ~ ! [X: $i] : ( p0(b,X) = true )
| ( p0(b,b) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
p0(b,b) = true,
inference(unit_resolution,[status(thm)],[130,129]) ).
tff(132,plain,
true = p0(b,b),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
m0(a,e,e) = p0(b,b),
inference(transitivity,[status(thm)],[117,132]) ).
tff(134,plain,
ifeq(m0(a,e,e),true,l2(e,e),true) = ifeq(p0(b,b),true,ifeq(m0(a,e,e),true,l2(e,e),true),true),
inference(monotonicity,[status(thm)],[133,122]) ).
tff(135,plain,
ifeq(p0(b,b),true,ifeq(m0(a,e,e),true,l2(e,e),true),true) = ifeq(m0(a,e,e),true,l2(e,e),true),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( ( m0(b,b,e) = true )
<=> ( m0(b,b,e) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,axiom,
m0(b,b,e) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).
tff(138,plain,
m0(b,b,e) = true,
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
m0(b,b,e) = m0(a,e,e),
inference(transitivity,[status(thm)],[138,118]) ).
tff(140,plain,
ifeq(m0(b,b,e),true,l2(e,e),true) = ifeq(m0(a,e,e),true,l2(e,e),true),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
ifeq(p0(b,b),true,ifeq(m0(b,b,e),true,l2(e,e),true),true) = ifeq(p0(b,b),true,ifeq(m0(a,e,e),true,l2(e,e),true),true),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
ifeq(p0(b,b),true,ifeq(m0(a,e,e),true,l2(e,e),true),true) = ifeq(p0(b,b),true,ifeq(m0(b,b,e),true,l2(e,e),true),true),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
ifeq(m0(a,e,e),true,l2(e,e),true) = ifeq(p0(b,b),true,ifeq(m0(b,b,e),true,l2(e,e),true),true),
inference(transitivity,[status(thm)],[134,142]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,s1(b),true) = s1(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
ifeq(true,true,s1(b),true) = s1(b),
inference(unit_resolution,[status(thm)],[144,16]) ).
tff(146,plain,
( ( q0(b,b) = true )
<=> ( q0(b,b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,axiom,
q0(b,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(148,plain,
q0(b,b) = true,
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
true = q0(b,b),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
ifeq(true,true,s1(b),true) = ifeq(q0(b,b),true,s1(b),true),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
ifeq(q0(b,b),true,s1(b),true) = ifeq(true,true,s1(b),true),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
q0(b,b) = p0(b,b),
inference(transitivity,[status(thm)],[148,132]) ).
tff(153,plain,
ifeq(q0(b,b),true,s1(b),true) = ifeq(p0(b,b),true,s1(b),true),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
ifeq(p0(b,b),true,s1(b),true) = ifeq(q0(b,b),true,s1(b),true),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
^ [I: $i] :
refl(( ( ifeq(p0(I,I),true,s1(I),true) = true )
<=> ( ifeq(p0(I,I),true,s1(I),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(156,plain,
( ! [I: $i] : ( ifeq(p0(I,I),true,s1(I),true) = true )
<=> ! [I: $i] : ( ifeq(p0(I,I),true,s1(I),true) = true ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [I: $i] : ( ifeq(p0(I,I),true,s1(I),true) = true )
<=> ! [I: $i] : ( ifeq(p0(I,I),true,s1(I),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,axiom,
! [I: $i] : ( ifeq(p0(I,I),true,s1(I),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_125) ).
tff(159,plain,
! [I: $i] : ( ifeq(p0(I,I),true,s1(I),true) = true ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [I: $i] : ( ifeq(p0(I,I),true,s1(I),true) = true ),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [I: $i] : ( ifeq(p0(I,I),true,s1(I),true) = true ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
( ~ ! [I: $i] : ( ifeq(p0(I,I),true,s1(I),true) = true )
| ( ifeq(p0(b,b),true,s1(b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
ifeq(p0(b,b),true,s1(b),true) = true,
inference(unit_resolution,[status(thm)],[162,161]) ).
tff(164,plain,
true = ifeq(p0(b,b),true,s1(b),true),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
p0(b,b) = s1(b),
inference(transitivity,[status(thm)],[131,164,154,151,145]) ).
tff(166,plain,
ifeq(p0(b,b),true,ifeq(m0(a,e,e),true,l2(e,e),true),true) = ifeq(s1(b),true,ifeq(p0(b,b),true,ifeq(m0(b,b,e),true,l2(e,e),true),true),true),
inference(monotonicity,[status(thm)],[165,143]) ).
tff(167,plain,
ifeq(s1(b),true,ifeq(p0(b,b),true,ifeq(m0(b,b,e),true,l2(e,e),true),true),true) = ifeq(p0(b,b),true,ifeq(m0(a,e,e),true,l2(e,e),true),true),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
^ [B: $i,A: $i,J: $i,C: $i] :
refl(( ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true )
<=> ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(169,plain,
( ! [B: $i,A: $i,J: $i,C: $i] : ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true )
<=> ! [B: $i,A: $i,J: $i,C: $i] : ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
( ! [B: $i,A: $i,J: $i,C: $i] : ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true )
<=> ! [B: $i,A: $i,J: $i,C: $i] : ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
! [B: $i,A: $i,J: $i,C: $i] : ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_133) ).
tff(172,plain,
! [B: $i,A: $i,J: $i,C: $i] : ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
! [B: $i,A: $i,J: $i,C: $i] : ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true ),
inference(skolemize,[status(sab)],[172]) ).
tff(174,plain,
! [B: $i,A: $i,J: $i,C: $i] : ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[173,169]) ).
tff(175,plain,
( ~ ! [B: $i,A: $i,J: $i,C: $i] : ( ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true )
| ( ifeq(s1(b),true,ifeq(p0(b,b),true,ifeq(m0(b,b,e),true,l2(e,e),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
ifeq(s1(b),true,ifeq(p0(b,b),true,ifeq(m0(b,b,e),true,l2(e,e),true),true),true) = true,
inference(unit_resolution,[status(thm)],[175,174]) ).
tff(177,plain,
true = ifeq(s1(b),true,ifeq(p0(b,b),true,ifeq(m0(b,b,e),true,l2(e,e),true),true),true),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
true = l2(e,e),
inference(transitivity,[status(thm)],[177,167,135,120,114]) ).
tff(179,plain,
ifeq(true,true,m4(e,e),true) = ifeq(l2(e,e),true,m4(e,e),true),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
ifeq(l2(e,e),true,m4(e,e),true) = ifeq(true,true,m4(e,e),true),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
m4(e,e) = ifeq(true,true,m4(e,e),true),
inference(symmetry,[status(thm)],[112]) ).
tff(182,plain,
m4(e,e) = ifeq(l2(e,e),true,m4(e,e),true),
inference(transitivity,[status(thm)],[181,179]) ).
tff(183,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,s3(a,e),true) = s3(a,e) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
ifeq(true,true,s3(a,e),true) = s3(a,e),
inference(unit_resolution,[status(thm)],[183,16]) ).
tff(185,plain,
( ( m0(e,d,e) = true )
<=> ( m0(e,d,e) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,axiom,
m0(e,d,e) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
tff(187,plain,
m0(e,d,e) = true,
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
true = m0(e,d,e),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
ifeq(true,true,s3(a,e),true) = ifeq(m0(e,d,e),true,s3(a,e),true),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
ifeq(m0(e,d,e),true,s3(a,e),true) = ifeq(true,true,s3(a,e),true),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(m0(e,d,e),true,s3(a,e),true),true) = ifeq(m0(e,d,e),true,s3(a,e),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
ifeq(true,true,ifeq(m0(e,d,e),true,s3(a,e),true),true) = ifeq(m0(e,d,e),true,s3(a,e),true),
inference(unit_resolution,[status(thm)],[191,16]) ).
tff(193,plain,
m0(a,e,e) = m0(e,d,e),
inference(transitivity,[status(thm)],[117,188]) ).
tff(194,plain,
ifeq(m0(a,e,e),true,s3(a,e),true) = ifeq(m0(e,d,e),true,s3(a,e),true),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
ifeq(m0(e,d,e),true,s3(a,e),true) = ifeq(m0(a,e,e),true,s3(a,e),true),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,q2(a,a,a),true) = q2(a,a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
ifeq(true,true,q2(a,a,a),true) = q2(a,a,a),
inference(unit_resolution,[status(thm)],[196,16]) ).
tff(198,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p1(a,a,a),true) = p1(a,a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
ifeq(true,true,p1(a,a,a),true) = p1(a,a,a),
inference(unit_resolution,[status(thm)],[198,16]) ).
tff(200,plain,
( ( l0(a) = true )
<=> ( l0(a) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,axiom,
l0(a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
tff(202,plain,
l0(a) = true,
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
true = l0(a),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
ifeq(true,true,p1(a,a,a),true) = ifeq(l0(a),true,p1(a,a,a),true),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
ifeq(l0(a),true,p1(a,a,a),true) = ifeq(true,true,p1(a,a,a),true),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
( ( ifeq(l0(a),true,p1(a,a,a),true) = true )
<=> ( ifeq(l0(a),true,p1(a,a,a),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,axiom,
ifeq(l0(a),true,p1(a,a,a),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_088) ).
tff(208,plain,
ifeq(l0(a),true,p1(a,a,a),true) = true,
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
true = ifeq(l0(a),true,p1(a,a,a),true),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
true = p1(a,a,a),
inference(transitivity,[status(thm)],[209,205,199]) ).
tff(211,plain,
ifeq(true,true,q2(a,a,a),true) = ifeq(p1(a,a,a),true,q2(a,a,a),true),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
ifeq(p1(a,a,a),true,q2(a,a,a),true) = ifeq(true,true,q2(a,a,a),true),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
^ [I: $i] :
refl(( ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true )
<=> ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(214,plain,
( ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true )
<=> ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ) ),
inference(quant_intro,[status(thm)],[213]) ).
tff(215,plain,
( ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true )
<=> ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(216,axiom,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_181) ).
tff(217,plain,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
inference(skolemize,[status(sab)],[217]) ).
tff(219,plain,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
inference(modus_ponens,[status(thm)],[218,214]) ).
tff(220,plain,
( ~ ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true )
| ( ifeq(p1(a,a,a),true,q2(a,a,a),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
ifeq(p1(a,a,a),true,q2(a,a,a),true) = true,
inference(unit_resolution,[status(thm)],[220,219]) ).
tff(222,plain,
true = ifeq(p1(a,a,a),true,q2(a,a,a),true),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
true = q2(a,a,a),
inference(transitivity,[status(thm)],[222,212,197]) ).
tff(224,plain,
ifeq(true,true,ifeq(m0(e,d,e),true,s3(a,e),true),true) = ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true),
inference(monotonicity,[status(thm)],[223,195]) ).
tff(225,plain,
ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true) = ifeq(true,true,ifeq(m0(e,d,e),true,s3(a,e),true),true),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
ifeq(m0(e,d,e),true,s3(a,e),true) = ifeq(true,true,ifeq(m0(e,d,e),true,s3(a,e),true),true),
inference(symmetry,[status(thm)],[192]) ).
tff(227,plain,
ifeq(m0(a,e,e),true,s3(a,e),true) = ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true),
inference(transitivity,[status(thm)],[194,226,224]) ).
tff(228,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,s2(a),true) = s2(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(229,plain,
ifeq(true,true,s2(a),true) = s2(a),
inference(unit_resolution,[status(thm)],[228,16]) ).
tff(230,plain,
true = s1(b),
inference(transitivity,[status(thm)],[164,154,151,145]) ).
tff(231,plain,
ifeq(true,true,s2(a),true) = ifeq(s1(b),true,s2(a),true),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
ifeq(s1(b),true,s2(a),true) = ifeq(true,true,s2(a),true),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
s2(a) = ifeq(true,true,s2(a),true),
inference(symmetry,[status(thm)],[229]) ).
tff(234,plain,
s2(a) = ifeq(s1(b),true,s2(a),true),
inference(transitivity,[status(thm)],[233,231]) ).
tff(235,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,q2(b,a,b),true) = q2(b,a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
ifeq(true,true,q2(b,a,b),true) = q2(b,a,b),
inference(unit_resolution,[status(thm)],[235,16]) ).
tff(237,plain,
^ [Y: $i,X: $i] :
refl(( ( m0(X,d,Y) = true )
<=> ( m0(X,d,Y) = true ) )),
inference(bind,[status(th)],[]) ).
tff(238,plain,
( ! [Y: $i,X: $i] : ( m0(X,d,Y) = true )
<=> ! [Y: $i,X: $i] : ( m0(X,d,Y) = true ) ),
inference(quant_intro,[status(thm)],[237]) ).
tff(239,plain,
( ! [Y: $i,X: $i] : ( m0(X,d,Y) = true )
<=> ! [Y: $i,X: $i] : ( m0(X,d,Y) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(240,axiom,
! [Y: $i,X: $i] : ( m0(X,d,Y) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
tff(241,plain,
! [Y: $i,X: $i] : ( m0(X,d,Y) = true ),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
! [Y: $i,X: $i] : ( m0(X,d,Y) = true ),
inference(skolemize,[status(sab)],[241]) ).
tff(243,plain,
! [Y: $i,X: $i] : ( m0(X,d,Y) = true ),
inference(modus_ponens,[status(thm)],[242,238]) ).
tff(244,plain,
( ~ ! [Y: $i,X: $i] : ( m0(X,d,Y) = true )
| ( m0(d,d,b) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
m0(d,d,b) = true,
inference(unit_resolution,[status(thm)],[244,243]) ).
tff(246,plain,
true = m0(d,d,b),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
ifeq(true,true,q2(b,a,b),true) = ifeq(m0(d,d,b),true,q2(b,a,b),true),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
ifeq(m0(d,d,b),true,q2(b,a,b),true) = ifeq(true,true,q2(b,a,b),true),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,n1(a,b,b),true) = n1(a,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
ifeq(true,true,n1(a,b,b),true) = n1(a,b,b),
inference(unit_resolution,[status(thm)],[249,16]) ).
tff(251,plain,
( ( p0(b,d) = true )
<=> ( p0(b,d) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(252,axiom,
p0(b,d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
tff(253,plain,
p0(b,d) = true,
inference(modus_ponens,[status(thm)],[252,251]) ).
tff(254,plain,
true = p0(b,d),
inference(symmetry,[status(thm)],[253]) ).
tff(255,plain,
ifeq(true,true,n1(a,b,b),true) = ifeq(p0(b,d),true,n1(a,b,b),true),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
ifeq(p0(b,d),true,n1(a,b,b),true) = ifeq(true,true,n1(a,b,b),true),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true )
| ( ifeq(n0(b,a),true,l1(a,a),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(258,plain,
ifeq(n0(b,a),true,l1(a,a),true) = true,
inference(unit_resolution,[status(thm)],[257,33]) ).
tff(259,plain,
( ( n0(b,a) = true )
<=> ( n0(b,a) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,axiom,
n0(b,a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
tff(261,plain,
n0(b,a) = true,
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
true = n0(b,a),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
ifeq(true,true,l1(a,a),true) = ifeq(n0(b,a),true,l1(a,a),true),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,l1(a,a),true) = l1(a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(265,plain,
ifeq(true,true,l1(a,a),true) = l1(a,a),
inference(unit_resolution,[status(thm)],[264,16]) ).
tff(266,plain,
l1(a,a) = ifeq(true,true,l1(a,a),true),
inference(symmetry,[status(thm)],[265]) ).
tff(267,plain,
l1(a,a) = p0(b,d),
inference(transitivity,[status(thm)],[266,263,258,254]) ).
tff(268,plain,
ifeq(l1(a,a),true,n1(a,b,b),true) = ifeq(p0(b,d),true,n1(a,b,b),true),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
ifeq(l1(a,a),true,n1(a,b,b),true) = n1(a,b,b),
inference(transitivity,[status(thm)],[268,256,250]) ).
tff(270,plain,
l0(a) = p0(b,d),
inference(transitivity,[status(thm)],[202,254]) ).
tff(271,plain,
ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,b,b),true),true) = ifeq(p0(b,d),true,n1(a,b,b),true),
inference(monotonicity,[status(thm)],[270,269]) ).
tff(272,plain,
ifeq(p0(b,d),true,n1(a,b,b),true) = ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,b,b),true),true),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
n1(a,b,b) = ifeq(true,true,n1(a,b,b),true),
inference(symmetry,[status(thm)],[250]) ).
tff(274,plain,
n1(a,b,b) = ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,b,b),true),true),
inference(transitivity,[status(thm)],[273,255,272]) ).
tff(275,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,n1(a,b,a),true) = n1(a,b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(276,plain,
ifeq(true,true,n1(a,b,a),true) = n1(a,b,a),
inference(unit_resolution,[status(thm)],[275,16]) ).
tff(277,plain,
( ( s0(b) = true )
<=> ( s0(b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(278,axiom,
s0(b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
tff(279,plain,
s0(b) = true,
inference(modus_ponens,[status(thm)],[278,277]) ).
tff(280,plain,
true = s0(b),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
ifeq(true,true,n1(a,b,a),true) = ifeq(s0(b),true,n1(a,b,a),true),
inference(monotonicity,[status(thm)],[280]) ).
tff(282,plain,
ifeq(s0(b),true,n1(a,b,a),true) = ifeq(true,true,n1(a,b,a),true),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(s0(b),true,n1(a,b,a),true),true) = ifeq(s0(b),true,n1(a,b,a),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
ifeq(true,true,ifeq(s0(b),true,n1(a,b,a),true),true) = ifeq(s0(b),true,n1(a,b,a),true),
inference(unit_resolution,[status(thm)],[283,16]) ).
tff(285,plain,
ifeq(true,true,ifeq(s0(b),true,n1(a,b,a),true),true) = ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),
inference(monotonicity,[status(thm)],[132]) ).
tff(286,plain,
ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true) = ifeq(true,true,ifeq(s0(b),true,n1(a,b,a),true),true),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),true) = ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(288,plain,
ifeq(true,true,ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),true) = ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),
inference(unit_resolution,[status(thm)],[287,16]) ).
tff(289,plain,
ifeq(true,true,ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),true) = ifeq(l0(a),true,ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),true),
inference(monotonicity,[status(thm)],[203]) ).
tff(290,plain,
ifeq(l0(a),true,ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),true) = ifeq(true,true,ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),true),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
^ [D: $i,E: $i] :
refl(( ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true )
<=> ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(292,plain,
( ! [D: $i,E: $i] : ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true )
<=> ! [D: $i,E: $i] : ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[291]) ).
tff(293,plain,
( ! [D: $i,E: $i] : ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true )
<=> ! [D: $i,E: $i] : ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(294,axiom,
! [D: $i,E: $i] : ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_050) ).
tff(295,plain,
! [D: $i,E: $i] : ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[294,293]) ).
tff(296,plain,
! [D: $i,E: $i] : ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true ),
inference(skolemize,[status(sab)],[295]) ).
tff(297,plain,
! [D: $i,E: $i] : ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[296,292]) ).
tff(298,plain,
( ~ ! [D: $i,E: $i] : ( ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true )
| ( ifeq(l0(a),true,ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(299,plain,
ifeq(l0(a),true,ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),true) = true,
inference(unit_resolution,[status(thm)],[298,297]) ).
tff(300,plain,
true = ifeq(l0(a),true,ifeq(p0(b,b),true,ifeq(s0(b),true,n1(a,b,a),true),true),true),
inference(symmetry,[status(thm)],[299]) ).
tff(301,plain,
p0(b,d) = n1(a,b,a),
inference(transitivity,[status(thm)],[253,300,290,288,286,284,282,276]) ).
tff(302,plain,
ifeq(p0(b,d),true,n1(a,b,b),true) = ifeq(n1(a,b,a),true,ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,b,b),true),true),true),
inference(monotonicity,[status(thm)],[301,274]) ).
tff(303,plain,
ifeq(n1(a,b,a),true,ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,b,b),true),true),true) = ifeq(p0(b,d),true,n1(a,b,b),true),
inference(symmetry,[status(thm)],[302]) ).
tff(304,plain,
^ [E: $i,F: $i,G: $i] :
refl(( ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true )
<=> ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(305,plain,
( ! [E: $i,F: $i,G: $i] : ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true )
<=> ! [E: $i,F: $i,G: $i] : ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[304]) ).
tff(306,plain,
( ! [E: $i,F: $i,G: $i] : ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true )
<=> ! [E: $i,F: $i,G: $i] : ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(307,axiom,
! [E: $i,F: $i,G: $i] : ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_054) ).
tff(308,plain,
! [E: $i,F: $i,G: $i] : ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[307,306]) ).
tff(309,plain,
! [E: $i,F: $i,G: $i] : ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true ),
inference(skolemize,[status(sab)],[308]) ).
tff(310,plain,
! [E: $i,F: $i,G: $i] : ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[309,305]) ).
tff(311,plain,
( ~ ! [E: $i,F: $i,G: $i] : ( ifeq(n1(E,F,E),true,ifeq(l0(G),true,ifeq(l1(G,E),true,n1(E,F,F),true),true),true) = true )
| ( ifeq(n1(a,b,a),true,ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,b,b),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(312,plain,
ifeq(n1(a,b,a),true,ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,b,b),true),true),true) = true,
inference(unit_resolution,[status(thm)],[311,310]) ).
tff(313,plain,
true = ifeq(n1(a,b,a),true,ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,b,b),true),true),true),
inference(symmetry,[status(thm)],[312]) ).
tff(314,plain,
m0(d,d,b) = n1(a,b,b),
inference(transitivity,[status(thm)],[245,313,303,256,250]) ).
tff(315,plain,
ifeq(m0(d,d,b),true,q2(b,a,b),true) = ifeq(n1(a,b,b),true,q2(b,a,b),true),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
ifeq(n1(a,b,b),true,q2(b,a,b),true) = ifeq(m0(d,d,b),true,q2(b,a,b),true),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true) = ifeq(n1(a,b,b),true,q2(b,a,b),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
ifeq(true,true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true) = ifeq(n1(a,b,b),true,q2(b,a,b),true),
inference(unit_resolution,[status(thm)],[317,16]) ).
tff(319,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p1(b,b,b),true) = p1(b,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
ifeq(true,true,p1(b,b,b),true) = p1(b,b,b),
inference(unit_resolution,[status(thm)],[319,16]) ).
tff(321,plain,
( ( p0(c,b) = true )
<=> ( p0(c,b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(322,axiom,
p0(c,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
tff(323,plain,
p0(c,b) = true,
inference(modus_ponens,[status(thm)],[322,321]) ).
tff(324,plain,
true = p0(c,b),
inference(symmetry,[status(thm)],[323]) ).
tff(325,plain,
ifeq(true,true,p1(b,b,b),true) = ifeq(p0(c,b),true,p1(b,b,b),true),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
ifeq(p0(c,b),true,p1(b,b,b),true) = ifeq(true,true,p1(b,b,b),true),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
^ [B: $i,C: $i] :
refl(( ( ifeq(p0(C,B),true,p1(B,B,B),true) = true )
<=> ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(328,plain,
( ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true )
<=> ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ) ),
inference(quant_intro,[status(thm)],[327]) ).
tff(329,plain,
( ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true )
<=> ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(330,axiom,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_085) ).
tff(331,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[330,329]) ).
tff(332,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(skolemize,[status(sab)],[331]) ).
tff(333,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[332,328]) ).
tff(334,plain,
( ~ ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true )
| ( ifeq(p0(c,b),true,p1(b,b,b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(335,plain,
ifeq(p0(c,b),true,p1(b,b,b),true) = true,
inference(unit_resolution,[status(thm)],[334,333]) ).
tff(336,plain,
true = ifeq(p0(c,b),true,p1(b,b,b),true),
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
true = p1(b,b,b),
inference(transitivity,[status(thm)],[336,326,320]) ).
tff(338,plain,
ifeq(true,true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true) = ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true) = ifeq(true,true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
ifeq(n1(a,b,b),true,q2(b,a,b),true) = ifeq(true,true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),
inference(symmetry,[status(thm)],[318]) ).
tff(341,plain,
ifeq(n1(a,b,b),true,q2(b,a,b),true) = ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),
inference(transitivity,[status(thm)],[340,338]) ).
tff(342,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,q2(a,b,b),true) = q2(a,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(343,plain,
ifeq(true,true,q2(a,b,b),true) = q2(a,b,b),
inference(unit_resolution,[status(thm)],[342,16]) ).
tff(344,plain,
( ( k0(b) = true )
<=> ( k0(b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(345,axiom,
k0(b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
tff(346,plain,
k0(b) = true,
inference(modus_ponens,[status(thm)],[345,344]) ).
tff(347,plain,
true = k0(b),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
ifeq(true,true,q2(a,b,b),true) = ifeq(k0(b),true,q2(a,b,b),true),
inference(monotonicity,[status(thm)],[347]) ).
tff(349,plain,
ifeq(k0(b),true,q2(a,b,b),true) = ifeq(true,true,q2(a,b,b),true),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(k0(b),true,q2(a,b,b),true),true) = ifeq(k0(b),true,q2(a,b,b),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(351,plain,
ifeq(true,true,ifeq(k0(b),true,q2(a,b,b),true),true) = ifeq(k0(b),true,q2(a,b,b),true),
inference(unit_resolution,[status(thm)],[350,16]) ).
tff(352,plain,
ifeq(true,true,ifeq(k0(b),true,q2(a,b,b),true),true) = ifeq(p1(a,a,a),true,ifeq(k0(b),true,q2(a,b,b),true),true),
inference(monotonicity,[status(thm)],[210]) ).
tff(353,plain,
ifeq(p1(a,a,a),true,ifeq(k0(b),true,q2(a,b,b),true),true) = ifeq(true,true,ifeq(k0(b),true,q2(a,b,b),true),true),
inference(symmetry,[status(thm)],[352]) ).
tff(354,plain,
^ [E: $i,F: $i] :
refl(( ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true )
<=> ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(355,plain,
( ! [E: $i,F: $i] : ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true )
<=> ! [E: $i,F: $i] : ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true ) ),
inference(quant_intro,[status(thm)],[354]) ).
tff(356,plain,
( ! [E: $i,F: $i] : ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true )
<=> ! [E: $i,F: $i] : ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(357,axiom,
! [E: $i,F: $i] : ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_177) ).
tff(358,plain,
! [E: $i,F: $i] : ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true ),
inference(modus_ponens,[status(thm)],[357,356]) ).
tff(359,plain,
! [E: $i,F: $i] : ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true ),
inference(skolemize,[status(sab)],[358]) ).
tff(360,plain,
! [E: $i,F: $i] : ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true ),
inference(modus_ponens,[status(thm)],[359,355]) ).
tff(361,plain,
( ~ ! [E: $i,F: $i] : ( ifeq(p1(E,E,E),true,ifeq(k0(F),true,q2(E,F,F),true),true) = true )
| ( ifeq(p1(a,a,a),true,ifeq(k0(b),true,q2(a,b,b),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(362,plain,
ifeq(p1(a,a,a),true,ifeq(k0(b),true,q2(a,b,b),true),true) = true,
inference(unit_resolution,[status(thm)],[361,360]) ).
tff(363,plain,
true = ifeq(p1(a,a,a),true,ifeq(k0(b),true,q2(a,b,b),true),true),
inference(symmetry,[status(thm)],[362]) ).
tff(364,plain,
p1(b,b,b) = ifeq(true,true,p1(b,b,b),true),
inference(symmetry,[status(thm)],[320]) ).
tff(365,plain,
p1(b,b,b) = q2(a,b,b),
inference(transitivity,[status(thm)],[364,325,335,363,353,351,349,343]) ).
tff(366,plain,
ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true) = ifeq(q2(a,b,b),true,ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),true),
inference(monotonicity,[status(thm)],[365,341]) ).
tff(367,plain,
ifeq(q2(a,b,b),true,ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),true) = ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),
inference(symmetry,[status(thm)],[366]) ).
tff(368,plain,
^ [H: $i,F: $i,G: $i] :
refl(( ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true )
<=> ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(369,plain,
( ! [H: $i,F: $i,G: $i] : ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true )
<=> ! [H: $i,F: $i,G: $i] : ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[368]) ).
tff(370,plain,
( ! [H: $i,F: $i,G: $i] : ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true )
<=> ! [H: $i,F: $i,G: $i] : ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(371,axiom,
! [H: $i,F: $i,G: $i] : ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_182) ).
tff(372,plain,
! [H: $i,F: $i,G: $i] : ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[371,370]) ).
tff(373,plain,
! [H: $i,F: $i,G: $i] : ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true ),
inference(skolemize,[status(sab)],[372]) ).
tff(374,plain,
! [H: $i,F: $i,G: $i] : ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[373,369]) ).
tff(375,plain,
( ~ ! [H: $i,F: $i,G: $i] : ( ifeq(q2(G,H,F),true,ifeq(p1(F,F,H),true,ifeq(n1(G,F,H),true,q2(F,G,F),true),true),true) = true )
| ( ifeq(q2(a,b,b),true,ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(376,plain,
ifeq(q2(a,b,b),true,ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),true) = true,
inference(unit_resolution,[status(thm)],[375,374]) ).
tff(377,plain,
true = ifeq(q2(a,b,b),true,ifeq(p1(b,b,b),true,ifeq(n1(a,b,b),true,q2(b,a,b),true),true),true),
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
s1(b) = ifeq(true,true,s1(b),true),
inference(symmetry,[status(thm)],[145]) ).
tff(379,plain,
s1(b) = q2(b,a,b),
inference(transitivity,[status(thm)],[378,150,153,163,377,367,339,318,316,248,236]) ).
tff(380,plain,
ifeq(s1(b),true,s2(a),true) = ifeq(q2(b,a,b),true,ifeq(s1(b),true,s2(a),true),true),
inference(monotonicity,[status(thm)],[379,234]) ).
tff(381,plain,
ifeq(q2(b,a,b),true,ifeq(s1(b),true,s2(a),true),true) = ifeq(s1(b),true,s2(a),true),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
^ [H: $i] :
refl(( ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true )
<=> ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(383,plain,
( ! [H: $i] : ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true )
<=> ! [H: $i] : ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true ) ),
inference(quant_intro,[status(thm)],[382]) ).
tff(384,plain,
( ! [H: $i] : ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true )
<=> ! [H: $i] : ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(385,axiom,
! [H: $i] : ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_189) ).
tff(386,plain,
! [H: $i] : ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true ),
inference(modus_ponens,[status(thm)],[385,384]) ).
tff(387,plain,
! [H: $i] : ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true ),
inference(skolemize,[status(sab)],[386]) ).
tff(388,plain,
! [H: $i] : ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true ),
inference(modus_ponens,[status(thm)],[387,383]) ).
tff(389,plain,
( ~ ! [H: $i] : ( ifeq(q2(b,H,b),true,ifeq(s1(b),true,s2(H),true),true) = true )
| ( ifeq(q2(b,a,b),true,ifeq(s1(b),true,s2(a),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
ifeq(q2(b,a,b),true,ifeq(s1(b),true,s2(a),true),true) = true,
inference(unit_resolution,[status(thm)],[389,388]) ).
tff(391,plain,
true = ifeq(q2(b,a,b),true,ifeq(s1(b),true,s2(a),true),true),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
q2(a,a,a) = ifeq(true,true,q2(a,a,a),true),
inference(symmetry,[status(thm)],[197]) ).
tff(393,plain,
q2(a,a,a) = s2(a),
inference(transitivity,[status(thm)],[392,211,221,391,381,232,229]) ).
tff(394,plain,
ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true) = ifeq(s2(a),true,ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true),true),
inference(monotonicity,[status(thm)],[393,227]) ).
tff(395,plain,
ifeq(s2(a),true,ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true),true) = ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
^ [I: $i,B: $i,A: $i,J: $i] :
refl(( ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true )
<=> ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(397,plain,
( ! [I: $i,B: $i,A: $i,J: $i] : ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true )
<=> ! [I: $i,B: $i,A: $i,J: $i] : ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[396]) ).
tff(398,plain,
( ! [I: $i,B: $i,A: $i,J: $i] : ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true )
<=> ! [I: $i,B: $i,A: $i,J: $i] : ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(399,axiom,
! [I: $i,B: $i,A: $i,J: $i] : ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_273) ).
tff(400,plain,
! [I: $i,B: $i,A: $i,J: $i] : ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[399,398]) ).
tff(401,plain,
! [I: $i,B: $i,A: $i,J: $i] : ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true ),
inference(skolemize,[status(sab)],[400]) ).
tff(402,plain,
! [I: $i,B: $i,A: $i,J: $i] : ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[401,397]) ).
tff(403,plain,
( ~ ! [I: $i,B: $i,A: $i,J: $i] : ( ifeq(s2(I),true,ifeq(q2(A,I,A),true,ifeq(m0(A,B,J),true,s3(I,J),true),true),true) = true )
| ( ifeq(s2(a),true,ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(404,plain,
ifeq(s2(a),true,ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true),true) = true,
inference(unit_resolution,[status(thm)],[403,402]) ).
tff(405,plain,
true = ifeq(s2(a),true,ifeq(q2(a,a,a),true,ifeq(m0(a,e,e),true,s3(a,e),true),true),true),
inference(symmetry,[status(thm)],[404]) ).
tff(406,plain,
l2(e,e) = s3(a,e),
inference(transitivity,[status(thm)],[121,119,134,166,176,405,395,225,192,190,184]) ).
tff(407,plain,
ifeq(l2(e,e),true,m4(e,e),true) = ifeq(s3(a,e),true,ifeq(l2(e,e),true,m4(e,e),true),true),
inference(monotonicity,[status(thm)],[406,182]) ).
tff(408,plain,
ifeq(s3(a,e),true,ifeq(l2(e,e),true,m4(e,e),true),true) = ifeq(l2(e,e),true,m4(e,e),true),
inference(symmetry,[status(thm)],[407]) ).
tff(409,plain,
^ [E: $i,F: $i,G: $i] :
refl(( ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true )
<=> ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(410,plain,
( ! [E: $i,F: $i,G: $i] : ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true )
<=> ! [E: $i,F: $i,G: $i] : ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true ) ),
inference(quant_intro,[status(thm)],[409]) ).
tff(411,plain,
( ! [E: $i,F: $i,G: $i] : ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true )
<=> ! [E: $i,F: $i,G: $i] : ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(412,axiom,
! [E: $i,F: $i,G: $i] : ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_279) ).
tff(413,plain,
! [E: $i,F: $i,G: $i] : ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true ),
inference(modus_ponens,[status(thm)],[412,411]) ).
tff(414,plain,
! [E: $i,F: $i,G: $i] : ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true ),
inference(skolemize,[status(sab)],[413]) ).
tff(415,plain,
! [E: $i,F: $i,G: $i] : ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true ),
inference(modus_ponens,[status(thm)],[414,410]) ).
tff(416,plain,
( ~ ! [E: $i,F: $i,G: $i] : ( ifeq(s3(a,E),true,ifeq(l2(G,F),true,m4(E,F),true),true) = true )
| ( ifeq(s3(a,e),true,ifeq(l2(e,e),true,m4(e,e),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(417,plain,
ifeq(s3(a,e),true,ifeq(l2(e,e),true,m4(e,e),true),true) = true,
inference(unit_resolution,[status(thm)],[416,415]) ).
tff(418,plain,
true = ifeq(s3(a,e),true,ifeq(l2(e,e),true,m4(e,e),true),true),
inference(symmetry,[status(thm)],[417]) ).
tff(419,plain,
true = m4(e,e),
inference(transitivity,[status(thm)],[418,408,180,112]) ).
tff(420,plain,
ifeq(true,true,m5(d,d),true) = ifeq(m4(e,e),true,m5(d,d),true),
inference(monotonicity,[status(thm)],[419]) ).
tff(421,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,m5(d,d),true) = m5(d,d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(422,plain,
ifeq(true,true,m5(d,d),true) = m5(d,d),
inference(unit_resolution,[status(thm)],[421,16]) ).
tff(423,plain,
m5(d,d) = ifeq(true,true,m5(d,d),true),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
m5(d,d) = true,
inference(transitivity,[status(thm)],[423,420,110,107,9]) ).
tff(425,plain,
( ( m5(d,d) != true )
<=> ( m5(d,d) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(426,axiom,
m5(d,d) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(427,plain,
m5(d,d) != true,
inference(modus_ponens,[status(thm)],[426,425]) ).
tff(428,plain,
$false,
inference(unit_resolution,[status(thm)],[427,424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN143-10 : TPTP v9.0.0. Released v7.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:29:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.77/0.94 % SZS status Unsatisfiable
% 0.77/0.94 % SZS output start Proof
% See solution above
% 0.80/0.99 % E exiting
%------------------------------------------------------------------------------